In mobile communication systems, there is a need to estimate and compensate for frequency offsets. These offsets can be caused by, e.g., low precision clocks or temperature variations, but also Doppler shifts generated when a user equipment is moving towards or away from a base station.
Thus, Automatic Frequency Control (AFC) algorithms are used to alleviate these problems. To estimate the frequency offset, different methods can be used, depending on the type of communication system.
In Orthogonal Frequency Division Multiplexing (OFDM), the frequency offset can, e.g., be estimated by comparing the phase change of received pilot symbols between two different symbols. Under the assumption that the channel is constant during that time, the frequency offset can be estimated by correlating two received pilot symbols. The argument of the result then gives the frequency offset. However, this argument will be a number between −π and π, and therefore the result will only be correct if the absolute value of the phase change between the two different symbols due to the frequency offset is less than π. Thus there is a limit to the frequency offset that can be detected for a given distance between the two different symbols. The larger the distance between the two different symbols is, the lower is the frequency offset that can be detected.
Thus if the distance between the two different symbols is large, the precision of the estimate is good. However, the larger the distance is, the lower the Nyquist frequency for the frequency offset is. The Nyquist frequency gives the highest frequency offset that can be estimated.
As an example, the pilots in Third Generation (3G) Long Term Evolution (3G LTE), which uses OFDM as multiple access technique in the downlink, could be placed on symbol 0 and 4 in each slot of seven symbols. Thus the shortest distance between two pilots is three symbols, and the Nyquist frequency, i.e. the highest frequency offset that can be estimated without exceeding the π limit for the absolute value of the phase change, can be calculated to 2.33 kHz. However, larger frequency offsets, which can thus not be correctly estimated, may well occur.
Thus to work in e.g. a high-speed train scenario, with Doppler frequencies of 1300 Hz with the base station close to the track, the algorithm has to be capable of rapid frequency changes. In particular, since the user equipment in order to conserve battery power may use cycles in which reception is discontinued, the frequency change can be viewed as a frequency jump of 2600 Hz between two measurements. The same applies for other communication systems in which a frequency offset is estimated from a phase change of a received signal over a given time span.
There is a need for an algorithm that is able to handle larger frequency offsets in communication systems.